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Karl Oeljeklaus; Matei Toma
Non-Kähler compact complex manifolds associated to number fields
(Variétés complexes compactes non kähleriennes associées à des corps de nombres)
Annales de l'institut Fourier, 55 no. 1 (2005), p. 161-171, doi: 10.5802/aif.2093
Article PDF | Reviews MR 2141693 | Zbl 1071.32017
Class. Math.: 32J18, 32M17
Keywords: Compact complex manifolds, algebraic number fields, algebraic units, locally conformally Kähler metrics

Résumé - Abstract

For algebraic number fields $K$ with $s>0$ real and $2t>0$ complex embeddings and ``admissible'' subgroups $U$ of the multiplicative group of integer units of $K$ we construct and investigate certain $(s+t)$-dimensional compact complex manifolds $X(K,U)$. We show among other things that such manifolds are non-Kähler but admit locally conformally Kähler metrics when $t=1$. In particular we disprove a conjecture of I. Vaisman.


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